膜厚测量仪工作原理

Filmetrics膜厚测量系统 THIN-FILM MEASUREMENT 薄膜测量 Introduction 介绍 Thin film 薄膜 Very thin layers of material that are deposited on the surface of another material (thin films) are extremely important to many technology-based industries. Thin films are widely used, for example, to provide passivation, insulating layers between conductors, diffusion barriers, and hardness coatings for scratch and wear resistance. The fabrication of integrated circuits consists primarily of the deposition and selective removal of a series of thin films. 沉积在另一种物质表面的非常薄的物质层，即薄膜，对许多基于技术工艺的行业是非常重要的。 薄膜有广泛地应用，例如提供导体间的钝化绝缘层、防扩散层、防止划伤和磨损的硬化层。集 成电路的生产就主要由一系列薄膜的沉积和选择性的去除组成。 Films typically used in thin-film applications range from a few atoms (1Å or 0.0001 pm) to 100 pm thick (the width of a human hair.) They can be formed by many different processes, including spin coating, vacuum evaporation, sputtering, vapor deposition, and dip coating. To perform the functions for which they were designed, thin films must have the proper thickness, composition, roughness, and other characteristics important to the particular application. These characteristics must often be measured, both during and after thin film fabrication. 典型应用中的薄膜厚度从几个原子级别（1Å或0.0001pm）到100pm（人类头发的厚度）不等。 薄膜可通过许多不同的方法形成，包括旋涂、真空蒸镀、溅射、气相沉积和浸涂。为了实现设 计时的功能，薄膜就必须具有合适的厚度、成分、粗糙度和其它特定应用中的重要特性。而这 些特性常常必须在薄膜制造过程中及之后进行测量。 The two main classes of thin film measurement are optical and stylus based techniques. Stylus measurements measure thickness and roughness by monitoring the deflections of a fine-tipped stylus as it is dragged along the surface of the film. Stylus instruments are limited in speed and accuracy, and they require a "step" in the film to measure thickness. They are often the preferred method when measuring opaque films, such as metals. 两类主要的薄膜测量是基于光学和探针的方法。探针法测量厚度及粗糙度是通过监测精细探针 划过薄膜表面时的偏移。探针法在测量速度和精度上受限，并且测量厚度时需要在薄膜里作一 个“台阶”。探针法通常是测量不透明薄膜（例如金属）的首选方法。 Optical techniques determine thin-film characteristics by measuring how the films interact with light. Optical techniques can measure the thickness, roughness, and optical constants of a film. Optical constants describe how light propagates through and reflects from a material. Once known, optical constants may be related to other material parameters, such as composition and band gap. 光学法是通过测量光与薄膜如何相互作用来检测薄膜的特性。光学法可以测量薄膜的厚度、粗 糙度及光学参量。光学参量用来描述光如何通过一种物质进行传播和反射。一旦得知光学参量， 就可以同其它重要参量（例如成分及能带）联系起来。 Optical techniques are usually the preferred method for measuring thin films because they are accurate, nondestructive, and require little or no sample preparation. The two most common optical measurement types are spectral reflectance and ellipsometry. Spectral reflectance measures the amount of light reflected from a thin film over a range of wavelengths, with the incident light normal (perpendicular) to the sample surface. Ellipsometry is similar, except that it measures reflectance at non-normal incidence and at two different polarizations. In general, spectral reflectance is much simpler and less expensive than ellipsometry, but it is restricted to measuring less complex structures. 由于光学法测量准确、无损、只需很少或根本不需要准备样品，所以光学法常常是测量薄膜的 首选方法。两类最常用的光学测量法是反射光谱法及椭圆偏光法。反射光谱法是让光正（垂直） 入射到样品表面，测量被薄膜表面反射回来的一定波长范围的光。椭圆偏光法测量的是非垂直 入射光的反射光及光的两种不同偏振态。一般而言，反射光谱法比椭圆偏光法更简单和经济， 但它只限于测量较不复杂的结构。 N and k Definitions N和k的定义 Optical constants (n and k) describe how light propagates through a film. In simple terms, the electromagnetic field that describes light traveling through a material at a fixed time is given by: 光学参量（n和k）描述了光通过薄膜如何进行传播。固定时间里通过一种物质的光传播的电磁 场可以简单表示为： where x is distance, λ is the wavelength of light, and n and k are the film's refractive index and extinction coefficient, respectively. The refractive index is defined as the ratio of the speed of light in a vacuum to the speed of light in the material. The extinction coefficient is a measure of how much' light is absorbed in the material. 其中：x是距离，λ 是光波长，n和k则是薄膜相应的折射率和消光系数。折射率是光在物质和真 空中传播速度的比值。消光系数是测量光在物质中被吸收了多少。 Spectral Reflectance Basics 光谱反射基础 Single Interface 单界面 Reflection occurs whenever light crosses the interface between different materials. The fraction of light that is reflected by an interface is determined by the discontinuity in n and k. For light reflected off of a material in air, 当光穿过不同物质的界面时，反射就发生了。通过界面反射的光的部分取决于n和k的不连续性。 对空气中的物质的反射光来讲： 。 To see how spectral reflectance can be used to measure optical constants, consider the simple case of light reflected by a single nonabsorbing material (k=O). Then: 为了了解反射光谱如何被用来测量光学参量，可以假设光被无吸收（k=0）的单一物质反射的简 单情形。则： Clearly, n of the material can be determined from a measurement of R. In real materials, n varies with wavelength (that is to say, real materials exhibit dispersion), but since the reflectance is known at many wavelengths, n at each of these wavelengths is also known, as shown here. 显然，物质的折射率n能够通过测量R来知晓。实际物质中，n 随光波长不同而变化（也就是说， 实际物质会发生色散），但由于在许多波长下的反射率已知，所以在这些波长下的每一个折射 率也就可知，如公式所示。 Multiple Interfaces 多层界面 Consider now a thin film on top of another material. In this case both the top and bottom of the film reflect light. The total amount of reflected light is the sum of these two individual reflections. Because of the wavelike nature of light, the reflections from the two interfaces may add together either constructively (intensities add) or destructively (intensities subtract), depending upon their phase relationship. Their phase relationship is determined by the difference in optical path lengths of the two reflections, which in turn is determined by thickness of the film, its optical constants, and the wavelength of the light. Reflections are in-phase and therefore add constructively when the light path is equal to one integral multiple of the wavelength of light. For light perpendicularly incident on a transparent film, this occurs when 2nd=iλ, 现在考虑在另一种物质上的一层薄膜，该情形下，薄膜的顶部和底部都反射光。反射光的总量 为两个界面独立反射光的叠加。由于光的波动性，两个界面的反射光可能干涉相长（强度增加） 或干涉相消（强度减小），这取决于它们的相位关系。它们的相位关系取决于两组反射光的光 程差，而光程差是由薄膜的厚度、光学参量及光的波长决定的。当光程差等于光波长的整数倍 时，两组反射光位相相同，因而干涉相长。对于光垂直入射到一个透明薄膜的情形，当2nd=iλ 时两组反射光干涉相长。 where d is the thickness of the film and i is an integer(the factor of two is due to the fact that the light passes through the film twice.). Conversely, reflections are out of phase and add destructively when the light path is one half of a wavelength different from the in-phase condition, or when 2nd=(i+½)λ. The qualitative aspects of these reflections may be combined into a single equation: From this, we can see that the reflectance of a thin film will vary periodically with l/wavelength, which is illustrated below. Also, thicker films will exhibit a greater number of oscillations over a given wavelength range, while thinner films will exhibit fewer oscillations, and oftentimes only part of an oscillation, over the same range. 其中，d是薄膜厚度，i 是整数（系数2是由于光两次穿过薄膜）。相反的，光程差为波长的一 半时，或当2nd=(i+½)λ时，两组反射光相位相反，因而干涉相消。反射率可组合为一个简单公 式： 从公式可以看出，薄膜的反射率周期性地随波长的倒数变化，如下图所示。同样的，在相同波 长下，厚的薄膜产生更多数量的振荡，而薄的薄膜则产生较少的振荡，通常只有一个振荡的一 部分。 Determining Film Properties from Spectral Reflectance 通过反射光谱法确定薄膜特性 The amplitude and periodicity of the reflectance of a thin film is determined by the film's thickness, optical constants, and other properties such as interface roughness. In cases where there is more than one interface, it is not possible to solve for film properties in closed form, nor is it possible to solve for n and k at each wavelength individually. In practice, mathematical models are used that describe n and k over a range of wavelengths using only a few adjustable parameters. A film's properties are determined by calculating reflectance spectra based on trial values of thickness and the n and k model parameters, and then adjusting these values until the calculated reflectance matches the measured reflectance. 薄膜反射率的振幅和周期取决于薄膜的厚度、光学参量及其它特性，如表面粗糙度。在超过一 个界面的情况下，不可能用一种紧密关联的形式来描述薄膜的特性，也不可能在每个单一波长 下描述 n 和 k 。实际中，常使用数学建模来描述一定波长范围里的n和k，只需几个可变量即 可。薄膜特性通过计算基于厚度实验值及n与k模型参量的反射光谱来确定，并且调整这些值， 直至计算的反射率和测量的反射率相匹配。 Models for n and k There are many models for describing n and k as a function of wavelength. When choosing a model for a particular film, it is important that the model be able to accurately describe n and k over the wavelength range of interest using as few parameters as possible. In general, the optical constants of different classes of materials (e.g., dielectrics, semiconductors, metals, and amorphous materials) vary quite differently with wavelength, and require different models to describe them (see below.) Models for dielectrics (k=0) generally have three parameters, while nondielectrics generally have five or more parameters. Therefore, as an example, to model the two-layer structure shown below, a total of 18 adjustable parameters must be considered in the solution. n和k的建模 n和k是波长的函数，可通过多种模型来描述。为某一特定薄膜选择模型时，使用尽可能少的变 量来准确地描述在相关波长范围内的n和k是非常重要的。总之，不同种类物质（例如：电介质、 半导体、金属和非晶体）的光学参数随波长有很大的不同，需要不同的模型来描述。电介质（k=0） 的模型通常有三个变量，而非电介质通常有五个或更多的变量。因此，作为例子，以下建立了 两层薄膜结构的模型，共考虑了18个可变量。 Cauchy： 42 )(   CB An  0)( k 待定量：A，B，C（共三个） 无定型半导体：        32,1 1 2222 0 2 2 0 2 1 )( )( 2)( 或j i ii giiii EECEE EEECA nkE if E>Eg，or=0 if E分析

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